Volume 8
Issue 3
Fisheries
JOURNAL OF
POLISH
AGRICULTURAL
UNIVERSITIES
Available Online: http://www.ejpau.media.pl/volume8/issue3/art06.html
AGE AS WELL AS LENGTH AND WEIGHT GROWTH OF CRUCIAN CARP FROM THE SZCZECIN LAGOON AND THE LESZCZYNSKIE LAKELAND
Agnieszka Rybczyk, Jerzy Szypuła
Department of Fish Biology,
Agricultural University of Szczecin, Poland
The study involved crucian carp harvested in various seasons of 20002002 from the Szczecin Lagoon (177 individuals) and from the Leszczyńskie Lakeland (707 individuals). The fish age was determined from scales. The length growth was backcalculated with the scale radiuscorrected Vovk method in which the standard length was set at 12 mm [10]. In addition, 5 mathematical growth models (FordWalford, von Bertalanffy, Gompertz, the second order polynomial, and modified power function) were applied. The weight growth was followed by means of the modified von Bertalanffy equation.
Key words: crucian carp, growth, mathematical growth models.
INTRODUCTION
Until the 1990s, the crucian carp had been treated as a commercially worthless species, almost as a fish pest. The situation changed with time. The species appeared in lakes of the southern part of the Wielkopolska region in Poland in the 1980s, at first accidentally, due to migrations, and later on it was intentionally introduced. As a result of lake stocking, the crucian carp began to feature in lake fish landings; initially fairly scant in catches, the landings became recordbreaking with time [12]. The crucian carp is turning out to be more and more important in Poland due to its tasty meat and a relatively low price. In addition, on account of its size, the species is an attractive target for anglers. The available literature contains few reports on the crucian carp; the scarcity of data on the species´ length and weight growth and on the fish conditions is particularly visible.
The crucian carp to be examined were harvested from the Szczecin Lagoon and from three lakes situated in the Leszczyńskie Lakeland.
The Szczecin Lagoon is a flowtrough lacustrine coastal water body. The Lagoon covers 910 km^{2 }(excluding Lake Dąbie); the mean and maximum depths are 3.8 and 6.5 m, respectively [5].
The three following Leszczyńskie Lakeland lakes were fished for the crucian carp:
Lake Wonieść, a reservoir formed in 19741982 from natural lakes and meadows, pastures, fields, woodland, and barren grounds between them, flooded as a result of earth dam constructions. In physicogeographical terms, the lakes making up the Wonieść reservoir belonged in the Krzywińskie Lakeland mesoregion, a part of the Leszczyńskie Lakeland macroregion. The Wonieść fills a narrow postglacial trough; it is 12.7 km long and 200 1300 m wide. The water surface area, including fish ponds, is 776.47 ha. The lakes making up the Wonieść belonged, in terms of their fisheries classification, to the zander (the Drzetowskie, Witosławskie, and Wojnowickie) and bream (the Jezierzyckie and the Woniewskie) lake types.
Lake Łoniewskie is a flowthrough basin located in the catchment of the Samica Osiecka. The lake covers 102 ha; its maximum and mean depths are 5.4 and 2.1 m, respectively. The latitudinally trending trough of the lake has a moderately complex shoreline, most of it is overgrown by a fairly narrow belt of shore vegetation. From the standpoint of fisheries typology, the lake is classified as a tenchpike one.
Lake Zbęchy is situated in the Rów Wyskoć catchment and covers 108.9 ha. The shoreline is not complex (WL=1.88). The maximum and mean depths are 8.5 and 4.3 m, respectively. The lake is 2610 m long, the maximum width is 725 m [4].
MATERIALS AND METHODS
The study involved examination of 884 crucian carp individuals harvested in 20002002 from the Szczecin Lagoon and from 3 lakes of the Leszczyńskie Lakeland. In the latter, the fish were obtained from spring and summer commercial catches effected with fyke nets and other traps, towed gear being used in autumnwinter. In the Szczecin Lagoon, the fish were harvested with fyke nets.
The Szczecin Lagoon crucian carp measured (standard length, longitudo corporis, l.c.) from 12.01 to 33.40 cm and weighed (total weight) from 52.60 to 1340.60 g (mean weight 464.80 g).
The Leszczyńskie Lakeland fish measured (l.c.) from 10.90 to 35.50 cm (mean length 24.27 cm) and weighed from 42.10 to 1850.00 g (mean weight 603.69 g).
The fish length growth rate was determined by back calculation involving scales. The fish lengthscale radius relationship was curvilinear (Fig. 1), for which reason the scale radius was corrected with the Vovk method (the standard length set at 12 mm).
Fig. 1. The LR relationship in the crucian carp 
The data obtained from back calculations were used to follow the crucian carp growth and to calculate the values of terms of the mathematical models describing the length and weight growth [11]. Because the crucian carp growth rate is relatively poorly known, 5 mathematical models were applied. The weight growth was modelled with the von Bertalanffy equation using weight data produced by converting the backcalculated lengths and applying the terms k and n of the lengthweight (LW) relationship. The relationship was determined with the commonly applied power function. Values of the terms K and t_{0} used were identical to those in the von Bertalanffy equation applied to the length growth.
RESULTS
The age distribution of the Szczecin Lagoon crucian carp showed domination of the fish aged 3 years (49 out of 177 individuals or 27.68%). The least numerous were the oldest (aged 7 and 6 years) individuals. The Leszczyńskie Lakeland crucian carp were dominated by the fish aged 4, 3, and 5 years (Table 1).
Table 1. Age distribution of the crucian carp in the Szczecin Lagoon and the Leszczyńskie Lakeland 
Age Water body 
1+ 
2+ 
3+ 
4+ 
5+ 
6+ 
7+ 
8+ 
9+ 
Total 
Szczecin Lagoon 
17 
34 
49 
36 
31 
9 
1 
177 

% 
9.60 
19.21 
27.68 
20.34 
17.51 
5.08 
0.56 
100 

Leszczyńskie Lakeland 
51 
89 
170 
193 
138 
48 
12 
4 
2 
707 
% 
7.21 
12.59 
24.05 
27.30 
19.52 
6.79 
1.70 
0.57 
0.28 
100 
The length distribution of the Szczecin Lagoon crucian carp (Table 2) showed domination of length classes 2628 and 2426 cm (33 and 30 individuals, respectively). The Leszczyńskie Lakeland crucian carp were dominated by the fish that were 2628 cm (221 individuals) and 2426 cm (166 individuals) long.
In terms of weight (Table 3), the Szczecin Lagoon sample was dominated by the 200300 g weight class (21.47%), the Leszczyńskie Lakeland fish showing domination of the 700800 g (17.27%) and 600700 g (15.78%) classes.
Table 2. Length growth rate of the crucian carp in the Szczecin Lagoon, calculated with the Vovk method for individual age groups 
Age group 
Standard length (l.c. cm) in individual years of life 

L_{1} 
L_{2} 
L_{3} 
L_{4} 
L_{5} 
L_{6} 
L_{7} 

I II III IV V VI VII 
11.33 11.75 11.83 12.66 11.50 12.15 11.65 
15.46 15.37 16.22 14.81 15.32 15.34 
18.37 19.64 17.91 18.12 19.58 
22.56 20.53 21.03 22.54 
23.37 23.39 25.27 
26.54 28.27 
31.16 
Mean 
11.89 
15.47 
18.61 
21.56 
23.42 
26.71 
31.16 
Increment 
11.89 
3.58 
3.14 
2.95 
1.86 
3.29 
4.45 
n 
177 
160 
126 
77 
41 
10 
1 
Table 3. Length growth rate of the crucian carp in the Leszczyńskie Lakeland, calculated with the Vovk method for individual age groups 
Age group 
Standard length (l.c. cm) in individual years of life 

L_{1} 
L_{2} 
L_{3} 
L_{4} 
L_{5} 
L_{6} 
L_{7} 
L_{8} 
L_{9} 

I II III IV V VI VII VIII IX 
11.45 11.23 12.87 12.53 12.55 12.15 12.12 12.68 11.44 
15.41 17.41 17.13 16.87 15.70 15.77 15.89 13.56 
21.14 20.62 19.85 18.30 18.55 18.81 16.19 
23.81 22.60 20.66 21.13 21.25 19.09 
24.95 22.91 23.02 23.63 21.50 
24.83 25.06 26.71 24.17 
27.39 28.43 25.91 
30.19 29.50 
30.41 
Mean 
12.35 
16.76 
20.27 
22.86 
24.23 
24.96 
27.49 
29.99 
30.41 
Increment 
12.35 
4.41 
3.51 
2.59 
1.37 
0.73 
2.53 
2.50 
0.42 
N 
805 
754 
661 
475 
250 
89 
23 
7 
2 
As shown by the data, the Szczecin Lagoon and the Leszczyńskie Lakeland crucian carp samples did not differ markedly in the length growth rates. The highest increments (11.89 and 12.35 cm, respectively) were observed in the first year of life, the increments in the subsequent 2 years being about 23 times lower. A further reduction of length increment, fairly similar in the two areas, was observed as the fish continued to grow.
The backcalculated data were used to calculate terms of 5 mathematical growth models:
1) the FordWalford model, 2) the von Bertalanffy equation, 3) the Gompertz model, 4) the second order polynomial, and 5) the modified power function.
Calculations of fish growth rates with the models listed were based on the 6 initial age classes in the Szczecin Lagoon fish (age group 7 was disregarded because it was represented by a single individual only) and on the first 7 age classes in the Leszczyńskie Lakeland (the fish aged 8 and 9 years were represented by as few as a total of 6 individuals).
The following forms of the models were used:
Szczecin Lagoon:
1) 
2) 
3) 
4) 
5) 
Leszczyńskie Lakeland:
1) 
2) 
3) 
4) 
5) 
As shown by the results obtained for the two areas (Szczecin Lagoon, Table 4; and Leszczyńskie Lakeland, Table 5), the models applied turned out to represent the crucian carp growth very adequately. In the Szczecin Lagoon, the best fit was obtained with the modified power function (the average absolute difference was as low as 0.18 cm), the von Bertalanffy equation providing the best fit in the Leszczyńskie Lakeland sample (the average absolute difference 0.35 cm). However, the modified power function and the Gompertz model produced values that only slightly deviated from the backcalculated ones (the average absolute difference of 0.38 cm in both cases). Much larger (and the most extensive) differences in both areas were produced by the FordWalford model (the average absolute differences averaged 1.33 and 0.99 cm in the Szczecin Lagoon and the Leszczyńskie Lakeland, respectively). It should be mentioned that the FordWalford model was the only model in which the theoretical growth curve started in the coordinate origin; consequently, the absolute length differences were higher than those in the remaining models applied.
Table 4. Length growth rate of the Szczecin Lagoon crucian carp, as calculated with different methods 
Age (years) 
Method 
12 
13 
14 
15 
16 

1 
2 
3 
4 
5 
6 

1 2 3 4 5 6 
11.89 15.47 18.61 21.56 23.42 26.71 
10.39 16.71 20.55 22.89 24.31 25.18 
12.04 15.37 18.46 21.33 24.00 26.47 
12.30 15.47 18.60 21.56 24.30 26.71 
12.05 15.36 18.46 21.34 24.00 26.45 
11.89 15.48 18.56 21.36 23.96 26.41 
1.50 1.24 1.94 1.33 0.89 1.53 
0.15 0.10 0.15 0.23 0.58 0.24 
0.41 0.00 0.01 0.00 0.88 0.00 
0.16 0.11 0.15 0.22 0.58 0.26 
0.00 0.01 0.05 0.20 0.54 0.30 
Average absolute difference 
1.31 
0.24 
0.22 
0.25 
0.18 
1.Back calculations, 2. FordWalford model, 3. von Bertalanffy equation, 4. Gompertz model, 5. Second order polynomial, 6. Modified power function. 
Table 5. Length growth rate of the Leszczyńskie Lakeland crucian carp, as calculated with different methods 
Age (years) 
Method 
12 
13 
14 
15 
16 

1 
2 
3 
4 
5 
6 

1 2 3 4 5 6 7 
12.35 16.76 20.27 22.86 24.23 24.96 27.49 
11.26 17.76 21.51 23.68 24.93 25.65 26.08 
12.48 16.71 19.97 22.48 24.41 25.89 27.03 
12.35 16.52 20.07 22.86 24.94 26.44 27.49 
12.69 16.58 19.84 22.50 24.54 25.97 26.79 
12.00 17.28 20.37 22.56 24.26 25.64 26.81 
1.09 1.00 1.24 0.82 0.70 0.69 1.41 
0.13 0.05 0.03 0.38 0.18 0.93 0.46 
0.00 0.24 0.20 0.00 0.71 1.48 0.00 
0.34 0.18 0.43 0.36 0.31 1.01 0.70 
0.35 0.52 0.10 0.30 0.03 0.68 0.68 
Average absolute difference 
0.99 
0.35 
0.38 
0.48 
0.38 
1.Back calculations, 2. FordWalford model, 3. von Bertalanffy equation, 4. Gompertz model, 5. Second order polynomial, 6. Modified power function. 
Figure 2 shows the lengthweight relationship in the crucian carp living in the Szczecin Lagoon and in the Leszczyńskie Lakeland. The power function calculated for the relationship assumed the form of :
Fig. 2. The lengthweight relationship in the crucian carp 
The relationship presented above was used to determine the crucian carp weight growth by converting backcalculated lengths to weights (the correlation coefficient was 0.99). The results obtained as well as the von Bertalanffy equation terms K and t_{0} were used to calculate weight growth of the crucian carp with the von Bertalanffy equation modified in the following way:
Szczecin Lagoon: 
Leszczyńskie Lakeland: 
Table 6 summarises results of weight growth calculations in the two areas. The data show that weight increments tended to increase with time and were fairly similar in both areas. Comparison of weight growth rates between the two areas showed the Leszczyńskie Lakeland fish to attain higher weight increments in the first two years of life; subsequently, the pattern was reversed so that decidedly higher weight increments were typical of the Szczecin Lagoon fish.
Table 6. Weight growth rate of crucian carp in the Szczecin Lagoon and the Leszczyńskie Lakeland 
Szczecin Lagoon 
Leszczyńskie Lakeland 

Weight from L to W conversion (g) 
Weight from modified von Bertalanffy equations (g) 
Average absolute difference (g) 
Weight from L to W conversion (g) 
Weight from modified von Bertalanffy equation (g) 
Average absolute difference (g) 

1 
61.5 
63.8 
2.3 
69.0 
71.2 
2.2 
2 
137.0 
134.4 
2.6 
174.9 
173.4 
1.5 
3 
240.5 
234.8 
5.7 
311.9 
298.2 
13.7 
4 
376.4 
364.5 
11.9 
449.8 
427.4 
22.4 
5 
484.2 
521.4 
37.2 
537.0 
549.0 
12.0 
6 
722.5 
702.5 
20.0 
587.8 
657.0 
69.2 
7 
788.6 
749.1 
39.5 

Average absolute difference 
13.3 
Average absolute difference 
22.9 
DISCUSSION
The fish age as well as the length and weight growth are important elements of knowledge on fish population biology. The crucian carp is generally known to have a moderately long life span, its average duration being 67 years. According to Kukuradze and Marijash [3], the crucian carp landings are dominated by the fish aged 3 and 4 years, which account for up to 60% of the catches. This observation was confirmed by this study which showed the two age groups to be most frequent in both areas: the two age groups accounted for 48.02 and 51.35% of the catches in the Szczecin Lagoon and the Leszczyńskie Lakeland, respectively.
When the mathematical growth models were applied to the entire material [8], including all the age groups represented in the samples (also the 7yearold individual from the Szczecin Lagoon and the six individuals aged 8 and 9 years from the Leszczyńskie Lakeland), the results obtained were markedly different from the data produced by backcalculations. The average absolute differences in each model were much higher, so disregarding the few oldest fish in this study can be considered a correct move. A poor representativeness of the materials may cause results of theoretical calculations to differ markedly from the backcalculated values and the growth pattern obtained may be misleading or imprecise.
Comparisons of the crucian carp length growth rates produced by the mathematical models with earlier data of various authors showed the von Bertalanffy equation to be the most commonly used model. According to Baruš and Lusk [1], Holčik [2], and Makara and Stráňaj [7], the increments in the first year were lower than those revealed by this study. The differences decrease slowly in the subsequent years. It was only the data reported by Makara [6] and by Kukuradze and Marijash [3] that showed the length growth rate to be much faster than that found in this study.
Analysis of the weight growth rate as calculated with the modified von Bertalanffy equation showed the weight in the first year of life to be much higher than the weight of the contemporaneous crucian carp studied by other authors: Makara and Stráňaj [7] reported their fish to weigh 16do 43 g in the first year of life; Sedlar et al. [9] found the crucian carp in the Dunajec, Nitra, and Zaluza to attain as little as 4.40, 6.20, and 4.10 g, respectively. In this study, the individual weight of the crucian carp in their first year of life was found to exceed 60 g.
CONCLUSIONS
Dominating age groups of crucian carp were fishes aged 3 and 4 years (both age groups accounted for 45% in Szczecin Lagoon and over 51% in Leszczynskie Lakeland).
The increment in growth during the first year of life was almost 3 times bigger than in the next years.
For the Szczecin Lagoon the most accurate mathematical model of growth appeared to be the Gompertz model, and for the Leszczynskie Lakeland  the von Bertalanffy equation.
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Agnieszka Rybczyk
Department of Fish Biology,
Agricultural University of Szczecin, Poland
Kazimierza Królewicza 4, 71550 Szczecin, Poland
email: wieski@fish.ar.szczecin.pl
Jerzy Szypuła
Department of Fish Biology,
Agricultural University of Szczecin, Poland
Kazimierza Królewicza 4, 71550 Szczecin, Poland
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